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3 years ago

Find the equation of the line perpendicular to y=-2/3x -7 that runs through the points (6,1) in slope intercept form

Mathematics

1 answer:

SVEN [57.7K]3 years ago

7 0

The equation of line is:

$y = \frac{3}{2}x-8$

Further explanation:

Given equation of line

$y=-\frac{2}{3}x-7$

Comparing it with the standard form

y = mx + b gives us:

slope = m1 = -2/3

Let m2 be the slope of second line

The product of slopes of two perpendicular lines is -1.

$m_1* m_2 = -1\\-\frac{2}{3} *m_2 = -1\\m_2 = -1 * -\frac{3}{2}\\m_2 = \frac{3}{2}\\Putting\ in\ standard\ form\\y = \frac{3}{2}x +b$

We have to find the value of b. So, Putting the point(6,1)

$1 = \frac{3}{2}(6) +b\\1 = (3 * 3) + b\\1=9+b\\1-9 =b\\b = -8\\The\ final\ equation\ is:\\y= \frac{3}{2}x -8$

Keywords: Coordinate geometry, Point-slope form

Learn more about coordinate geometry at:

#LearnwithBrainly

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Answer:

leah is going to diie due to a forest fire

Step-by-step explanation:

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2 years ago

Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Find the probability that (a)

UNO [17]

Answer:

a) P=0.226

b) P=0.6

c) P=0.0008

d) P=0.74

Step-by-step explanation:

We know that the seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Therefore, we have 46 balls.

a) We calculate the probability that are 3 red, 2 blue, and 2 green balls.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations:

$C_3^{12}\cdot C_2^{16}\cdot C_2^{18}=660\cdot 120\cdot 153=12117600$

Therefore, the probability is

$P=\frac{12117600}{53524680}\\\\P=0.226$

b) We calculate the probability that are at least 2 red balls.

We calculate the probability withdrawn of 1 or none of the red balls.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations: for 1 red balls

$C_1^{12}\cdot C_7^{34}=12\cdot 1344904=16138848$

Therefore, the probability is

$P_1=\frac{16138848}{53524680}\\\\P_1=0.3$

We calculate the number of favorable combinations: for none red balls

$C_7^{34}=5379616$

Therefore, the probability is

$P_0=\frac{5379616}{53524680}\\\\P_0=0.1$

Therefore, the the probability that are at least 2 red balls is

$P=1-P_1-P_0\\\\P=1-0.3-0.1\\\\P=0.6$

c) We calculate the probability that are all withdrawn balls are the same color.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations:

$C_7^{12}+C_7^{16}+C_7^{18}=792+11440+31824=44056$

Therefore, the probability is

$P=\frac{44056}{53524680}\\\\P=0.0008$

d) We calculate the probability that are either exactly 3 red balls or exactly 3 blue balls are withdrawn.

Let X, event that exactly 3 red balls selected.

$P(X)=\frac{C_3^{12}\cdot C_4^{34}}{53524680}=0.57\\$

Let Y, event that exactly 3 blue balls selected.

$P(Y)=\frac{C_3^{16}\cdot C_4^{30}}{53524680}=0.29\\$

We have

$P(X\cap Y)=\frac{18\cdot C_3^{12} C_3^{16}}{53524680}=0.12$

Therefore, we get

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)\\\\P(X\cup Y)=0.57+0.29-0.12\\\\P(X\cup Y)=0.74$

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3 years ago

Peter is giving marbles to some children at a carnival. He has 5 red marbles, 4 blue marbles, and 3 yellow marbles. If Peter sel

DENIUS [597]

P(blue marble)=2/6
p(yellow marble)=1/4
p(yellow&blue marble)=2/6+1/4=1/3

4 0

3 years ago

Which sequence of transformations carries ABCD onto HGFE?

Korvikt [17]

D.

Look at top left coordinate (2,-1)
Eight units left = (2-8,-1) = (-6,-1)
Reflection across x axis means change in y
(-6,-1) to (-6, 1) :)

6 0

2 years ago

I need help fast... if answered Correctly I will mark brainliest

Lesechka [4]

9514 1404 393

Answer:

(-5,1)

Step-by-step explanation:

To eliminate x, multiply the first equation by 3 and add 2 times the second equation.

3(-2x +7y) +2(3x -4y) = 3(17) +2(-19)

-6x +21y +6x -8y = 51 -38

13y = 13

y = 1 . . . . . matches the third answer choice

(x, y) = (-5, 1)

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3 years ago